The invention relates generally to the field of haptics. Specifically, the invention relates to a system and method for providing substantially stable control in a system using a virtual tool.
The field of haptics relates to, among other things, human interactive devices that provide tactile and/or force feedback to a user to achieve a desired goal. Tactile feedback may include providing a user with tactile sensations such as, for example, vibration. Force feedback may include providing various forms of force to a user, such as a positive force or a resistance to movement.
A common use of haptics is to provide a user of a device with guidance or limits for manipulation of that device. For example, the device may be a robotic system having an object, such as a physical tool, for performing a specified function. The user's manipulation of the physical tool can be guided or limited through the use of haptics to provide feedback to the user during manipulation of the physical tool.
Often such guidance is provided by using a computer to create a virtual environment that effectively guides or limits manipulation of the physical tool. The computer may create an association between the physical tool and a virtual tool (a virtual representation of the physical tool) in the virtual environment. The computer also may construct a haptic object within the virtual environment. The haptic object may provide boundaries for guiding or limiting movement of the virtual tool. For example, when the virtual tool interacts with a boundary of the haptic object, tactile or force feedback may be provided to the user. The guidance or limitation resulting from the interaction between the virtual tool and the haptic object effectively provides guidance or limitation for the user's manipulation of the physical tool.
A specific example of such a robotic system using haptics can be found in computer-assisted surgical systems. In such systems, a physical tool, such as a bone-cutting tool, may be associated with a virtual tool in a virtual environment. A pre-operative surgical plan may be used to identify a region for bone resection, which will then be used to create a haptic object in the virtual environment. For example. the haptic object may represent the boundaries of the bone-resection region. The surgeon will receive tactile or force feedback when the virtual tool interacts with the boundaries of the haptic object. This feedback can assist the surgeon in maintaining the bone-cutting tool with the bone-resection region, according to his/her pre-operative plan.
Feedback is generated based on the interaction of the virtual tool with the haptic object. A fundamental relationship often established for haptics is a linear elastic spring, where the contact force applied by the haptic object may be defined by the spring constant, K, and the displacement into the haptic object, Δx, such that{right arrow over (f)}=KΔ{right arrow over (x)}
To determine the appropriate feedback, the computer is usually able to determine the interaction between the virtual tool and the haptic object. This interaction is often determined by identifying a single haptic interaction point (HIP) that will represent the location of the virtual tool. For example, a HIP may be defined as the center of a spherical culling tool, as long as the haptic object is offset from a resection depth by the radius of the tool. In such cases, the computer uses the relationship between the HIP and the haptic object to determine the interaction of the virtual tool with the haptic object.
In certain circumstances, a single HIP may not be fully effective for determining the interaction between the virtual tool and the haptic object. For example, an irregular-shaped virtual tool may not be adequately represented by a single HIP. Due to the irregular shape of the virtual tool, a single HIP may not adequately account for variations on the cutting surface of the tool and/or rotation of the tool. In this case, multiple HIPs may be defined along the con tour of the virtual tool. For example, as shown in FIG. 2, three HIPs 20 (points 1, 2, and 3) may be defined on the outer edge of a virtual tool 10 to provide a better estimation of the interaction between the virtual tool and the haptic object.
Even multiple HIPs may not be fully effective for determining the interaction between the virtual tool and the haptic object. For example, traditional multi-point haptic forces may not be stable because of the competing forces that exist along a bi-lateral constraint such as a plane or line. In the example illustrated in FIG. 2, the irregular-shaped virtual tool 10 has outer HIPs (points 1 and 3) and an inner HIP (point 2). The outer HIPs are in an antagonistic relationship, such that haptic forces determined from the interaction of those outer HIPs (points 1 and 3) with the boundary 40 of the haptic object are in opposite directions, leading to an undesirable oscillation about a haptic plane. This unstable behavior can be attributed to measurement noise, discretization errors, and the competing forces between contact points.
The same unstable behavior may be present in other systems that provide non-haptic force feedback or control of a surgical tool using one or more interaction points.
In view of the foregoing, a need exists for a system and method that can provide substantially stable control for a control object that will correct undesirable oscillation caused by behavior such as measurement noise, discretization errors, and competing forces between interaction/contact points.